Impact of spatial dimension on spatio-temporal pattern formations

Swadesh Pal

Physica A: Statistical Mechanics and its Applications, 2025, vol. 668, issue C

Abstract: The study of prey–predator interactions has been a cornerstone in understanding ecological dynamics. Traditional models have primarily focused on one or two-dimensional spatial representations. However, many organisms move in three dimensions, significantly influencing species interaction dynamics and pattern formation. In this research, we explore the formation of spatial patterns in a prey–predator system within one, two and three spatial dimensions. Utilizing a system of reaction–diffusion equations, we analyse the conditions under which various spatial patterns emerge, including Turing patterns. Through numerical simulations, we demonstrate how three-dimensional spatial dynamics can lead to complex and rich patterns not observable in one or two-dimensional models. In addition, we explore the influence of initial conditions, parameter variations, and mode sections on pattern diversity. Furthermore, we have obtained gyroid-type patterns in a three-dimensional spatial domain that create a highly interconnected network of spaces analogous to the interconnected habitats in an ecosystem, which does not occur in a lower-dimensional domain. These findings provide insights into the underlying mechanisms driving spatial organization in ecological systems and contribute to the broader understanding of pattern formation in three-dimensional environmental and biological contexts.

Keywords: Phytoplankton; Zooplankton; Pattern formation; Zero mode; Turing mode; Three-dimension (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437125002171
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:668:y:2025:i:c:s0378437125002171

DOI: 10.1016/j.physa.2025.130565

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().